Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n, h;
double total, base = 1.0, one, low = 0.0, high, mid, area = 0.0;
double ans, a, single;
void solve(double a) {
  double low = 0, high = h, new_base;
  int time = 10000;
  while (time--) {
    mid = (low + high) / 2.0;
    new_base = mid / h;
    area = 0.5 * new_base * mid;
    if (area > a) {
      high = mid;
    } else if (area < a) {
      low = mid;
    }
  }
  printf("%.10lf ", mid);
}
int main() {
  scanf("%d%d", &n, &h);
  total = (0.5 * base * h);
  one = total / n;
  n--;
  a = one;
  while (n--) {
    solve(a);
    a += one;
  }
  return 0;
}